If you click on where it says "disABILTIES" at the top of this page it will take you to the Index. One of the top items is the "disABILTIES FAQ" which will gives lots of useful information. In Post #3 there is a section concerning dietary restrictions with both information and links.
However, this information is intended for people with food allergies. All of the eateries, both quick (counter) service and table service have vegetarian items available. You can look at the menus and other information by clicking on "DINING" near the very top of any DisBoards page, including this one. When you go to a table service restaurant you can ask your server for more information. If you are going to a buffet, you can ask one of the people working behind the counters for details.
Or, if you want an easier route to the FAQs, click on the link in my signature.